Increasing attention to the closed-loop supply chain and considering forward /reverse logistics has led to the presentation of various mathematical models in this field. This paper first presents a robust model for a supply chain network with forward /reverse flow approach, and then uses the experiment design method to determine the effect of each of the robust modeling parameters and the parameters of cost, production rate, return of products in the top and bottom level. this paper presents a new robust optimized model for the supply chain network.design The use of robust mathematical design and experimental modeling at the same time, which is done for the first time in this paper, has caused: 1) to increase the speed of achieving optimal answers, 2) to help the decision maker in the appropriate choice of model parameters in a structured way. The report and the presented results, according to the information of iron and steel industry, show the efficiency of using experimental design in order to reduce the time of solving the mathematical model and providing guidelines to the decision maker in the strategic area of supply chain.
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